Problem: Multiply the following complex numbers: $({-3+3i}) \cdot ({3-2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+3i}) \cdot ({3-2i}) = $ $ ({-3} \cdot {3}) + ({-3} \cdot {-2}i) + ({3}i \cdot {3}) + ({3}i \cdot {-2}i) $ Then simplify the terms: $ (-9) + (6i) + (9i) + (-6 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -9 + (6 + 9)i - 6i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -9 + (6 + 9)i - (-6) $ The result is simplified: $ (-9 + 6) + (15i) = -3+15i $